Vertical Curve Calculator
Analyze a parabolic vertical curve used in road design — find the K value and the high or low point’s location and elevation.
What is a Vertical Curve?
In road and site design, a vertical curve is the smooth parabolic transition used to connect two straight grade lines (like a downhill road becoming an uphill road) so vehicles don’t experience an abrupt change in slope.
The Method
The grade change is A = g2 – g1 (in percent). The K value, used by designers to check stopping sight distance, is K = L ÷ |A|, where L is the curve length. The station of the curve’s high or low point (measured from the PVC, the point of vertical curvature where the curve begins) is found from x = -g1 × L ÷ A, and its elevation is y = Elevation(PVC) + (g1/100)x + (A/100)(x² ÷ 2L).
A curve is a sag (valley) when A is positive and a crest (hilltop) when A is negative. If the calculated high/low point falls outside the curve length, the elevation is monotonic across the curve and the reported point is clamped to the nearer endpoint.
This tool is for general planning and educational purposes — final roadway geometry should be verified by a qualified civil engineer against applicable design standards (such as AASHTO).